How to merge all the faces
Ok, here is a crazy idea. As I said above in comments, "your file, frankly it's a bit a mess... around 50% faces have inverted normals, and so many of them are overlapping (not just crossing) in so many weird ways... I guess you didn't build this by hand... whatever was the tool, it did an horrible job.."

But, if you really like this shape you have now, except it's made from a spaghetti mess of dozens of separate "roads", and you wish to have a single connected mesh instead, here is how you could do it.

To do what it came to my mind, you need to export this 2D object as SVG, then use another tool, like Inkscape, to make the union in 2D, then reimport the united SVG in blender, as a single curve object that you could convert again to mesh (ALT-C) and thus have a single, connected mesh. I told you it was crazy...!

Except... blender has no svg export...

Wait, but there's a freestyle svg export addon!

Here is what I did. 


I used "blender render" instead of cycles, aiming for better speeds.
I activated the freestyle svg export
I enabled freestyle and the freestyle svg export for the scene
I used an orthographic camera (with sufficiently high orthographic scale) to render the whole "road" puzzle
I set a very high render resolution (3840x 2160) but I'm not sure it's really needed
then I hit F12 and waited the render to finish
after the normal render, freestyle adds a contour to the rendered objects: the freestyle svg export addon converts the freestyle outline to svg...


when the render finished, I found a 0001.svg file in /tmp, 

then I opened that svg in Inkscape and, after some cleaning, I used the Inkscape "union" command. Then saved the new svg, and inmported in Blender. Here is the result:



a closer look



in edit mode:



Here is the file:


You could need to repeat and master this until satisfied, but at least you now have a way...